Percolation in Networks with Voids and Bottlenecks
Abstract
A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled checkerboard and "stack-of-triangle" lattices. Thresholds for the checkerboard lattices of different mesh sizes are estimated using the gradient percolation method, while for the triangular system they are found exactly using the triangle-triangle transformation. The values of the thresholds approach the asymptotic values of 0.64222 and 0.53993 respectively as the mesh is made finer, consistent with a direct determination based upon the predicted critical corner-connection probability.
Cite
@article{arxiv.0811.4575,
title = {Percolation in Networks with Voids and Bottlenecks},
author = {Amir Haji-Akbari and Robert M. Ziff},
journal= {arXiv preprint arXiv:0811.4575},
year = {2009}
}
Comments
to appear, Physical Review E. Small changes from first version